I think Epsilon-delta proofs and I should spend some quality time together.

The problem is I need to prove that:

$\displaystyle \lim_{x \to -\infty} a^x = 0$

So, I need to show that, for every $\displaystyle \epsilon > 0$, there is a $\displaystyle \delta$ such that $\displaystyle |f(x) - L| < \epsilon$ whenever $\displaystyle x < \delta$.

So, given $\displaystyle \epsilon > 0$, I need to find $\displaystyle \delta$ such that:

$\displaystyle |a^x - 0| < \epsilon$ whenever $\displaystyle x < \delta$

And here's where I am stuck. I think I'll have to take a log in there somewhere. Wish my textbook wasn't so scarce on examples (Stewart's Calculus 4th edition). I sort of get limits where x->c, but I'm totally lost on the ones with infinities, and the differences between handling + and - infinities. Can't find any examples online of ones as x-> -infinity, which surely might help. Nor are the two videos at Khan Academy useful in this case.

I bet you guys get a lot of these. Surprisingly confusing for what seems a relatively simple concept, at first. Help, hints, pointers, nudges and taunts all appreciated.